A simplified analysis of transverse ply cracking in cross-ply laminates

This paper presents a method of analyzing transverse crack initiation and multiplication in symmetric cross-ply laminates. The method is based on the concept of a through-the-thickness inherent flaw and the energy balance principle. With a second-order polynomial assumed for the crack opening displacement, the perturbed stress field due to the presence of ply cracks is determined from the equilibrium conditions. The energy released as a result of ply cracking is then calculated and used to predict the increase in crack density. Based on an experimental correlation of the analytical result, a resistance curve is proposed to be used as a measure of the resistance to crack multiplication. The resistance to crack multiplication is shown to increase with the increasing crack density.     

Failure initiation in composite structures under low-velocity impact: Analytical studies

This paper presents an analytical model for the response of rectangular, specially orthotropic, symmetric laminated composite plates simply supported on all four sides subjected to low-velocity impact at the midpoint of the plate. The analysis is based considering both global and local effects. The influence of through-the-thickness normal stress on the magnitudes of inplane stresses is also considered. The plate is impacted by an impactor with a hemispherical tip. Contact force at the impact point, lateral displacements and velocities of the plate and the impactor and the stress state within the plate have been determined using modal solution technique. The governing equations, which apply to small deflection elastic response of specially orthotropic laminates, include combined effects of shear deformation and rotary inertia and non-linear Hertzian contact law. Inplane and interlaminar failure functions have been determined using quadratic failure criteria. Based on failure functions, damage initiation in the form of yarn/fiber breakage has been predicted. In general, it is observed that overall failure function is lower for woven fabric composites than for crossply laminates made of unidirectional layers.     

Ply cracking and stiffness degradation in cross-ply laminates under biaxial extension, bending and thermal loading

Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson’s ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods.     

DCB test simulation of stitched CFRP laminates using interlaminar tension test results

A simulation model for the delamination extension of stitched CFRP laminates and 3-D orthogonal interlocked fabric composites (3-D OIFC) has been developed using a 2-D finite element method incorporating interlaminar tension test results to simulate the experimental results of their DCB tests. The mechanical properties of through-the-thickness fiber were determined from the results of interlaminar tension tests in which the specimen included only one through-the-thickness yarn. The fracture phenomena around the through-the-thickness thread, such as debonding from the in-plane layer, slack absorption, fiber bridging, and the pull-out of broken threads from the in-plane layers, are also introduced into the FEM model. The present FEM simulation results were compared to DCB test results for certain stitched laminates and a 3-D OIFC, and the simulation results showed good agreement with the experimental results of DCB tests, including the load–displacement curve and Mode I strain energy release rate (GI). While it was difficult to estimate GI accurately when the DCB test specimen included different types of z-fiber fracture modes, the present model of FEM analysis can simulate the experimental results of DCB tests of stitched laminates and 3-D OIFC. It is suggested that the GI of CFRP with arbitrary z-fiber densities can be predicted by using this FEM analysis model together with interlaminar tension test results.     

Analytical prediction of damage due to large mass impact on thin ply composites

This article presents analytical models for predicting large mass impact response and damage in thin-ply composite laminates. Existing models for large mass impact (quasi-static) response are presented and extended to account for damage phenomena observed in thin-ply composites. The most important addition is a set of criteria for initiation and growth of bending induced compressive fibre failure, which has been observed to be extensive in thin ply laminates, while it is rarely observed in conventional laminates. The model predictions are compared to results from previous tests on CFRP laminates with a plain weave made from thin spread tow bands. The experiments seem to confirm the model predictions, but also highlight the need to include the effects of widespread bending induced fibre failure into the structural model.     

The influence of ply sequence and thermoelastic stress field on asymmetric delamination crack growth behavior of embedded elliptical delaminations in laminated FRP composites

The influence of ply lay up and the interaction of residual thermal stresses and mechanical loading on the interlaminar asymmetric embedded delamination crack growth behavior have been investigated. Two sets of full three-dimensional thermo-elastic finite element analyses have been performed for the interlaminar elliptical delaminations, which may be due to manufacturing defects or other reasons and are located symmetrically with respect to the midplane in a quasi-isotropic FRP composite laminate lay up. Depending upon the through-the-thickness location of the embedded elliptical delaminations, four different laminate configurations have been considered. Strain energy release rate (SERR) procedures have been employed to assess the delamination crack growth characteristics at the interfaces. It is found that the individual fracture modes exhibit asymmetric and non self-similar crack growth behavior along the delamination front depending upon the location of the interfacial delaminations; ply sequence and orientation and thermo-elastic anisotropy of the laminae.     

Interlaminar stresses in general thick rectangular laminated plates under in-plane loads

Three-dimensional multi-term extended Kantorovich method (3-D multi-term EKM) is employed to investigate analytically the interlaminar stresses near free edges of finite length general composite laminates subjected to axial and shearing loads. Using the principle of minimum total potential energy, three systems of coupled ordinary differential equations are obtained. Then an iterative procedure is established to achieve analytical solution. Laminates with finite dimensions are considered and full three-dimensional stresses in the interior and the boundary-layer regions are calculated. The results obtained from this theory are compared with those of analytical results existing in the literature or with those obtained by the finite element method when there exist no available results. It is found that interlaminar stresses have excellent agreements with those obtained by layerwise theory in the interior region and near the free edges of both finite and long laminates. Convergence study of the method reveals that the 3-D multi-term EKM converges within only four terms of trial functions and the single-term EKM is not able to estimate the local interlaminar stresses near the boundaries of laminates. Finally, the power of the present approach in obtaining the interlaminar stresses in finite length thick laminated plates with general lay-ups is examined.     

Stress distribution modeling for interference-fit area of each individual layer around composite laminates joint

The discussion about nonuniform stress distribution around interference-fit joint is particular significance in the design of composite laminates structures. In order to investigate the stress distribution of interference-fit area around composite laminates joint, an analytical model is developed for stress distribution based on the Lekhnitskii's complex potential theory. The normal and tangential stresses of contact are achieved by the relationship of deformation between pin and hole. The effects of ply orientation and interference percentage on stress components distributions of each individual layer around symmetrical laminates joint are discussed. In order to verify the validity of the analytical model, extensive 3D finite element models are established to simulate the stress components of laminates interference-fit joint. The results show that the analytical model is valid, and the laminate property and ply orientation have a significant effect on stress distribution trend while interference percentage mainly affects stress magnitude.     

Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading

The interlaminar stresses and displacements near the free-edges and ply cracks are investigated by using the state space equation method for general cross-ply laminates subjected to extension and/or thermal loading. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. Numerical solutions are compared with results obtained from other methods. It is found that the theory provides a satisfactory approximation to the stress singularity occurring in the vicinity of the free-edges and ply cracks.     

一种改进的内聚力损伤模型在复合材料层合板低速冲击损伤模拟中的应用

针对传统内聚力损伤模型(CZM)无法考虑层内裂纹对界面分层影响的缺点,提出了一种改进的适用于复合材料层合板低速冲击损伤模拟的CZM。通过对界面单元内聚力本构模型中的损伤起始准则进行修正,考虑了界面层相邻铺层内基体、纤维的损伤状态及应力分布对层间强度和分层扩展的影响。基于ABAQUS用户子程序VUMAT,结合本文模型及层合板失效判据,建立了模拟复合材料层合板在低速冲击作用下的渐进损伤过程的有限元模型,计算了不同铺层角度和材料属性的层合板在低速冲击作用下的损伤状态。通过数值模拟与试验结果的对比,验证了本文方法的精度及合理性。     

Numerical investigation to prevent crack jumping in Double Cantilever Beam tests of multidirectional composite laminates

During the experimental characterization of the mode I interlaminar fracture toughness of multidirectional composite laminates, the crack tends to migrate from the propagation plane (crack jumping) or to grow asymmetrically, invalidating the tests.The aim of this study is to check the feasibility of defining the stacking sequence of Double Cantilever Beam (DCB) specimens so that these undesired effects do not occur, leading to meaningful onset and propagation data from the tests. Accordingly, a finite element model using cohesive elements for interlaminar delamination and an intralaminar ply failure criterion are exploited here to thoroughly investigate the effect of specimen stiffness and thermal residual stresses on crack jumping and asymmetric crack growth occurring in multidirectional DCB specimens.The results show that the higher the arm bending stiffness, the lower the tendency to crack jumping and the better the crack front symmetry. This analysis raises the prospect of defining a test campaign leading to meaningful fracture toughness results (onset and propagation data) in multidirectional laminates.     

Design of experiments for stacking sequence optimizations with genetic algorithm using response surface approximation

This study describes a new method of experimental design to obtain a response surface of buckling load of laminated composites. Many evaluations for genetic algorithms for stacking sequence optimizations require high computational cost. That evaluation cost can be reduced by an approximation using a response surface. For a response surface for stacking sequence optimizations, lamination parameters are adopted as variables of the approximation function of the entire design space instead of ply angles for each ply. This study presents, proposes and investigates a new method of experimental design in detail. For most analytical tools, stacking sequences is demand as input data and lamination parameters cannot be applied directly to the tools. Therefore, the present study proposes and applies a new D-optimal set of laminates to the stacking sequence optimizations of the problem of maximization of buckling load of a composite cylinder. The new experimental design is a set of stacking sequences selected from candidate stacks using D-optimality. Consequently, the D-optimal set of laminates is shown to be effective for design of experiments of response surfaces for maximization of the buckling load of composite structures.     

热塑性复合材料层合板的层间应力与损伤机理

使用有限元生成软件FEPG和表征热塑性复合材料AS4/PEEK非线性行为和应变率相关行为的三维粘塑性模型,计算了复合材料角铺设层合板在单向拉伸时的界面层间应力.层间应力的三维分布图表明,AS4/PEEK对称角铺设层合板的层间剪应力在自由边缘处存在很明显的自由边缘效应;层间正应力也存在自由边缘效应,对于轴向拉伸,其在自由边缘处的值为负.随着铺设角的增大,自由边缘处二者的值均减小.层间应力存在端头效应,甚至比边缘效应还明显.随着铺设角的增大,层间应力在两端头处的值降低,层间正应力由压应力变为拉应力.主要由纤维控制的角铺设AS4/PEEK层合板,在自由边缘处较大的层间剪应力是引起其层间分层的主要原因;主要由基体控制的角铺设AS4/PEEK层合板,其首先产生的是面内应力破坏,而不是层间分层.     

Influence of woven ply degradation on fatigue crack growth in thin notched composites under tensile loading

This paper deals with the fatigue of the through-the-thickness crack propagation in thin notched composite laminates made of two glass woven plies. It highlights the different crack growths between warp and weft directions of the woven ply. Experimental results show a decrease of the crack growth rate per cycle with the increase of the crack initiation time. Moreover, it has been shown that it is necessary to take into account the fatigue damage of the woven plies in term of loss of rigidity in the initiation phase. The fatigue crack growth rates are then quantified using Paris law type equations and linear elastic fracture mechanics (LEFM).     

Modelling off-axis ply matrix cracking in continuous fibre-reinforced polymer matrix composite laminates

The fracture process of composite laminates subjected to static or fatigue tensile loading involves sequential accumulation of intra- and interlaminar damage, in the form of transverse cracking, splitting and delamination, prior to catastrophic failure. Matrix cracking parallel to the fibres in the off-axis plies is the first damage mode observed. Since a damaged lamina within the laminate retains certain amount of its load-carrying capacity, it is important to predict accurately the stiffness properties of the laminate as a function of damage as well as progression of damage with the strain state. In this paper, theoretical modelling of matrix cracking in the off-axis plies of unbalanced symmetric composite laminates subjected to in-plane tensile loading is presented and discussed. A 2-D shear-lag analysis is used to determine ply stresses in a representative segment and the equivalent laminate concept is applied to derive expressions for Mode I, Mode II and the total strain energy release rate associated with off-axis ply cracking. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

Fracture simulation of CFRP laminates in mixed mode bending

This paper analyses the progressive mixed mode delamination failure in unidirectional and multidirectional composite laminates using fracture experiments, finite element (FE) simulations and an analytical solution. The numerical model of the laminate is described as an assembly of damageable layers and bilinear interface elements subjected to mixed mode bending. The analytical approach is used to estimate the total mixed mode and decomposed fracture energies for laminates with different stacking sequences, which is also validated through experiments. It is concluded that the interlaminar fracture toughness of multidirectional laminates is considerably higher than that of the unidirectional ones. The effect of initial interfacial stiffness and element size is studied and it is also shown that their value must not exceed a definite limit for the numerical simulations to converge. The model can also be further extended to simulate the mixed mode fracture in hybrid fiber metal laminates.     

Effect of damage on the interlaminar shear properties of hybrid composite laminates at cryogenic temperatures

This paper presents the experimental and numerical characterization of the interlaminar shear failure of hybrid composite laminates at cryogenic temperatures. Cryogenic short beam shear tests were performed on hybrid laminates consisting of woven glass fiber reinforced polymer (GFRP) composites and polyimide films to evaluate their interlaminar shear strength. Microscopic observations of damage accumulation and failure mechanisms were also made on failed specimens. In addition, a progressive damage analysis was conducted to predict the initiation and growth of damage in the specimens, and the interlaminar shear strength was determined from the maximum shear stress in the failure region. The damage effect on the interlaminar shear properties of hybrid laminates at cryogenic temperatures was examined based on the experimental and numerical results.     

In situ measurements of through-the-thickness strains during processing of AS4/8552 composite

A novel approach has been developed to measure in situ the through-the-thickness strains during processing of epoxy composites. The technique captures the thermal expansion during the heating stages, the laminate consolidation throughout the cure process, and also the cure shrinkage. The tests were performed on 45 mm × 45 mm × 4 mm samples, for both unidirectional and cross-ply laminates. A ply pull-out technique was used to determine the position of the gel point of the AS4–8552 composite system for various curing temperatures. The relationship between the chemical shrinkage and the degree of cure was deduced from a cure kinetics model. Finally the relative contributions of cure shrinkage, thermal expansion and consolidation to the through-thickness strain were distinguished.     

Hybrid titanium–CFRP laminates for high-performance bolted joints

This paper presents an experimental and numerical investigation of the mechanical response of bolted joints manufactured using new hybrid composite laminates based on the substitution of CFRP plies with titanium plies. The local hybridization of the material is proposed to increase the efficiency of the bolted joints in CFRP structures. Two modeling strategies, based on non-linear finite element methods, are proposed for the analysis of the bolt-bearing and transition regions of the hybrid laminates. The bolt-bearing region is simulated using a three-dimensional finite element model that predicts ply failure mechanisms, whereas the free-edge of the transition region is simulated using plane stress and cohesive elements. The numerical and experimental results indicate that the use of hybrid composites can drastically increase the strength of CFRP bolted joints and therefore increase the efficiency of this type of connection. In addition, the numerical models proposed are able to predict the failure mechanisms and the strength of hybrid composite laminates with a good accuracy.     

Identifying through-thickness material properties of carbon-fiber-reinforced plastics using the virtual fields method combined with moiré interferometry

An investigation into the use of a novel curved-beam composite specimen is conducted to measure the interlaminar (through-thickness) tensile properties of carbon-fiber-reinforced plastic. A combination of a numerical model and full-field displacement/strain measurement with moiré interferometry is utilized in this study. Through-thickness material properties are identified from the measured displacement distribution using the virtual fields method. Because of the shape and the loading condition of the proposed curved composite beam, both tensile and shear stresses exist in the through-the-thickness direction. Therefore, the interlaminar tensile modulus, as well as the interlaminar shear modulus, can be evaluated. The measurement results by moiré interferometry provide the material properties through inverse analysis.